diff --git a/Lib/ipaddress.py b/Lib/ipaddress.py
index 1f900583826..20f33cbdeb6 100644
--- a/Lib/ipaddress.py
+++ b/Lib/ipaddress.py
@@ -636,12 +636,12 @@ def __getitem__(self, n):
         broadcast = int(self.broadcast_address)
         if n >= 0:
             if network + n > broadcast:
-                raise IndexError
+                raise IndexError('address out of range')
             return self._address_class(network + n)
         else:
             n += 1
             if broadcast + n < network:
-                raise IndexError
+                raise IndexError('address out of range')
             return self._address_class(broadcast + n)
 
     def __lt__(self, other):
diff --git a/Lib/test/test_ipaddress.py b/Lib/test/test_ipaddress.py
index be62fadf0d9..6c08f805da5 100644
--- a/Lib/test/test_ipaddress.py
+++ b/Lib/test/test_ipaddress.py
@@ -1176,6 +1176,7 @@ def testNth(self):
 
         self.assertEqual(str(self.ipv6_network[5]),
                          '2001:658:22a:cafe::5')
+        self.assertRaises(IndexError, self.ipv6_network.__getitem__, 1 << 64)
 
     def testGetitem(self):
         # http://code.google.com/p/ipaddr-py/issues/detail?id=15
diff --git a/Misc/NEWS b/Misc/NEWS
index 8c85c21b185..acf1a2e760f 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -38,6 +38,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #20508: Improve exception message of IPv{4,6}Network.__getitem__.
+  Patch by Gareth Rees.
+
 - Issue #21386: Implement missing IPv4Address.is_global property.  It was
   documented since 07a5610bae9d.  Initial patch by Roger Luethi.